A FEW WORDS ABOUT TELESCOPING SUMS Say that you want to
... The sum of the entries on the left hand side of these equalities is n·(n+1) · · · (n+k)/(k +1) and the sum of the entries on the right hand side of these equalities is 1 · 2 · · · k + 2 · 3 · · · (k + 1) + 3 · 4 · · · (k + 2) + · · · + n · (n + 1) · · · (n + k − 1), therefore the two expressions are ...
... The sum of the entries on the left hand side of these equalities is n·(n+1) · · · (n+k)/(k +1) and the sum of the entries on the right hand side of these equalities is 1 · 2 · · · k + 2 · 3 · · · (k + 1) + 3 · 4 · · · (k + 2) + · · · + n · (n + 1) · · · (n + k − 1), therefore the two expressions are ...
GCF
... The Greatest Common Factor (GCF) of 2 or more numbers is the largest number that can divide into all of the numbers. ...
... The Greatest Common Factor (GCF) of 2 or more numbers is the largest number that can divide into all of the numbers. ...
Subtraction
... can’t take a bigger number away from a smaller number.” Or “You have to put the bigger number first (in the minuend).” ...
... can’t take a bigger number away from a smaller number.” Or “You have to put the bigger number first (in the minuend).” ...
1 BASIC COUNTING RULES
... and no matter how the first thing happens, a second thing can happen in n2 ways, and so on, no matter how the first k − 1 things happen, a k-th thing can happen in nk ways, then all the k things together can happen in n1 × n2 × . . . × nk ways. Example 1.1 A local telephone number is given by a sequ ...
... and no matter how the first thing happens, a second thing can happen in n2 ways, and so on, no matter how the first k − 1 things happen, a k-th thing can happen in nk ways, then all the k things together can happen in n1 × n2 × . . . × nk ways. Example 1.1 A local telephone number is given by a sequ ...
Prime Time 1.6
... “made up of different parts”? • Did you know that factor means “one thing that influences or contributes to another”? • How do these everyday meanings related to their math meanings? ...
... “made up of different parts”? • Did you know that factor means “one thing that influences or contributes to another”? • How do these everyday meanings related to their math meanings? ...
Chapter 1
... Adding two positive integers: Add the digits and keep the sign Adding two negative integers: Add the digits and keep the sign Adding a positive and a negative integer: Subtract the smaller from the larger digit (disregarding the signs) and keep the sign of the larger digit (if the sign is disr ...
... Adding two positive integers: Add the digits and keep the sign Adding two negative integers: Add the digits and keep the sign Adding a positive and a negative integer: Subtract the smaller from the larger digit (disregarding the signs) and keep the sign of the larger digit (if the sign is disr ...
Addition
Addition (often signified by the plus symbol ""+"") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.The addition of two whole numbers is the total amount of those quantities combined. For example, in the picture on the right, there is a combination of three apples and two apples together; making a total of 5 apples. This observation is equivalent to the mathematical expression ""3 + 2 = 5"" i.e., ""3 add 2 is equal to 5"".Besides counting fruits, addition can also represent combining other physical objects. Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices.In arithmetic, rules for addition involving fractions and negative numbers have been devised amongst others. In algebra, addition is studied more abstractly.Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some non-human animals. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.